Bouchard, seeded sixth in the tournament, led 5-2 in the second set, but Cornet fought back before the ninth-ranked Canadian closed it out.
World's No. 3 Petra Kvitova, seeded third in Wuhan, also won, 6-3, 6-4 over Carolina Garcia of France.
The Czech southpaw, who prevailed over Bouchard in the final at Wimbledon, took only one hour 21 minutes to whisk aside Garcia.
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